A quick primer on repairing PCBs-
1) Get a magnifying glass, go over the both sides and search for broken traces (embedded tiny wires that connect components). Something simple as a small ding or scratch can break a connection and prevent the pcb from even powering up. If you find a broken trace, you will need to be handy with soldering and build a jumper wire to hop over the broken area. This involves using some 22Awg wire, a real tiny solder tip and a steady hand. Its best to tack on to a component from each side so you have something to solder to rather than trying from the trace itself.
Also as you stated about missing items- just because components are missing doesn't necessarily mean they were removed. Many times boards are made and re-used for different applications which don't take advantage of all the component spots. But since yours is a boot, they might be missing...
2) Cleaning - helps my tip above. Main areas would be edge connector, any fans/heat sinks and RAM/ROM sockets.
3) RAM/ROMs - Another easy thing to do is reset all your RAM and ROM chips. Get a flat blade screw driver and carefully pry up on each one to remove it from the socket. Inspect each for corrosion and damage, and dirt. Use contact cleaner on the pins and be careful to not bend them. Make sure you set it back in the same position you removed it from in the same orientation.
4) Continuity test - Get a multimeter and set it to check continuity. Then start tracing your voltage lines to make sure nothings breaking down. You can also check your diodes here too measuring their resistance. It really helps if you have a schematic of the board to really identify probelms. Since you have a boot, thats not an option.
Honestly, in the end you have to think about time spent versus time spent trying to fixing the game for what its worth. I realized this once upon a time trying to fix a MK2. I probably spent around some 30 hours with that thing and never fixed it.. I thought of all the things I could have done to easily paid for a new one many times over in that same time I wasted. Since this is Street Fighter II, I would just buy another pcb, they are very cheap and easy to find... aside form a few jerks on ebay who are hoarding boards and overcharging. Also, again because its a bootleg, its going to be tough to find any documentation for it to help support your troubleshooting.
Good luck!